Abstract

We introduce an extended transfer matrix method (TMM) for solving guided modes in leaky optical fibers with layered cladding. The method can deal with fibers with circular but nonconcentric material interfaces. Validity of the method is verified by two full-vector numerical methods. The TMM is then used to investigate the guidance property of perturbed Bragg fibers. Our analysis reveals that the core modes will interact with each other when a perturbed Bragg fiber has only C1 symmetry. Special attention is paid to the first transverse-electric (TE01) mode, which is found to experience severe degradation around spectral regions where its dispersion curve supposedly crosses a transverse-magnetic (TM) or hybrid mode.

Convergence of the neff value with respect to m. Inset, the fiber under test. The core has index n1 = 1.45. The first cladding layer has index n2 = 1.42. The outer cladding shares the same index as the core. The inner two interfaces have radii at 5μm and 10μm respectively, and their centers are displaced by ΔO = 3μm in y (vertical) direction.

Dispersion (a) and loss (b) curves for ten modes found in the unperturbed Bragg fiber whose structure is described in the text. In (a), the light-gray region is the TE cladding bandgap; the dark-gray region is the TM cladding bandgap. Notice the TM bandgap is “imersed” in the TE bandgap. Omni-reflection wavelength range (1.560~1.841μm) for the cladding stack is also indicated.

Dispersion (a) and loss (b) curves for the TE01 mode as ΔO changes. In (a), the TM and TE cladding bandgaps for the unperturbed fiber cladding are shaded in light- and dark-gray, respectively, m = 8 is used for all calculations, (c), (d), and (e) are loss spectra resulted from fine scans for the TE01 mode in the perturbed Bragg fiber with ΔO = 0.04μm.

The TE01 modes at wavelengths of 1.5775μm (a), 1.57769μm (b), 1.577726μm (c), 1.577738μm (d), 1.57775μm (e), 1.57777μm (f), 1.5778μm (g), and 1.5779μm (h), as indicated by the black markers in Fig. 8(b). The Ez field is also shown in (b).

Dispersion (a) and loss (b) curves for the TE01 mode as ΔO changes. In (a), TM cladding bandgap is shaded in light-gray; TE cladding bandgap is shaded in dark-gray. m = 3 is used for calculation when ΔO = 0.05μm, while m = 5 is used for calculation when ΔO = 0.10 μm.